A small spherical ball of radius $0.1 \,mm$ and density $10^{4} \,kg m ^{-3}$ falls freely under gravity through a a distance $h$ before entering a tank of water. If after entering the water the velocity of ball does not change and it continue to fall with same constant velocity inside water, then the value of $h$ wil be $m$. (Given $g =10 \,ms ^{-2}$, viscosity of water $=1.0 \times 10^{-5} \,N - sm ^{-2}$ )

Spherical balls of radius $ 'r'$  are falling in a viscous fluid of viscosity '$\eta$' with a velocity $ 'v'. $ The retarding viscous force acting on the spherical ball is

What is the velocity $v$  of a metallic ball of radius $r$  falling in a tank of liquid at the instant when its acceleration is one-half that of a freely falling body ? (The densities of metal and of liquid are $\rho$ and $\sigma$ respectively, and the viscosity of the liquid is $\eta$).

Small water droplets of radius $0.01 \mathrm{~mm}$ are formed in the upper atmosphere and falling with a terminal velocity of $10 \mathrm{~cm} / \mathrm{s}$. Due to condensation, if $8 \mathrm{such}$ droplets are coalesced and formed a larger drop, the new terminal velocity will be ........... $\mathrm{cm} / \mathrm{s}$.

The terminal velocity $\left( v _{ t }\right)$ of the spherical rain drop depends on the radius ( $r$ ) of the spherical rain drop as

An air bubble of radius $r$ rises steadily through a liquid of density $\rho $ with velocity $v$ . The coefficient of viscosity of liquid is